Question

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1. The following data represent the level of happiness and level of health for a random sample of people. Does the evidence suggest that health and happiness are related at the a = 0.05 level? Health Excellent 271 247 Good 261 Fair 82 231 Poor 20 53 567 Happiness Very Happy Pretty Happy Not Too Happy 33 103 92 36 a. Highlight the words or phrases that tell you what type of hypothesis test to perform. b. What is the significance level? c. Write your hypotheses. I d. Find the expected counts and write them in the table below. Excellent Good Fair Poor Very Happy Pretty Happy Not Too Happy e. Check the condition(s). - Previous Next

Answer 1

a) chi square test

b) level of significance = 0.05

c) ho: health an happiness are not related

ha: health an happiness are not related

d)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	h	g	f	p			Total
vh	551*634/1996=175.017	931*634/1996=295.718	405*634/1996=128.642	109*634/1996=34.622			634
ph	551*1098/1996=303.105	931*1098/1996=512.143	405*1098/1996=222.791	109*1098/1996=59.961			1098
nth	551*264/1996=72.878	931*264/1996=123.138	405*264/1996=53.567	109*264/1996=14.417			264
Total	551	931	405	109			1996

e) expected frequencies are greter than 5

f)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   182.1737
  
Level of Significance =   0.05
Number of Rows =   3
Number of Columns =   4
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 4- 1 ) =   6
  
p-Value =   0.0000

g) reject ho

h) there is enough evidence that health and happinesss are related